The Mole Concept: Empirical and Molecular Formulas, Molar Mass, and Mass Percent

Ch.8 The Mole Concept

Empirical Formula vs. Molecular Formula

The empirical formula of a compound represents the simplest whole-number ratio of the elements present, while the molecular formula shows the actual number of each type of atom in a molecule of the compound.

• Empirical Formula: Simplest ratio of elements in a compound (e.g., CH2O for glucose).

• Molecular Formula: Actual number of atoms of each element in a molecule (e.g., C6H12O6 for glucose).

• All chemical formulas must use whole numbers for each atom, representing the simplest ratio.

Example: For C6H12O6 (glucose), the empirical formula is CH2O.

Calculating the Empirical Formula

1. Write the symbols for each element present.

2. Write the mass (in grams) of each element. If given percentages, assume 100 g of compound.

3. Convert all masses to moles using atomic masses.

4. Divide each mole value by the smallest number of moles to get a whole-number ratio.

5. If necessary, multiply all ratios by a factor to obtain whole numbers (if values are not close to whole numbers).

Example: A compound is 68.40% chromium and 31.60% oxygen. Find the empirical formula.

Practice Problems

• Given 48.64% C and 43.2% O by mass (rest is H), find the empirical formula.

• Given 2.82 g Na, 4.35 g Cl, and 7.83 g O, find the empirical formula of the ionic compound.

• Given 4.19 x 1023 H atoms and 55.0% Cl by mass in 9.00 g of a compound (with C, H, Cl), find the empirical formula.

Molecular Formula

The molecular formula gives the actual number of each type of atom in a molecule. It is a whole-number multiple of the empirical formula.

• To determine the molecular formula, you need the empirical formula and the molar mass of the compound.

Calculating the Molecular Formula

1. Determine the empirical formula as above.

2. Calculate the empirical formula mass (sum of atomic masses in the empirical formula).

3. Divide the molar mass of the compound by the empirical formula mass to get the n-factor:

$n = \frac{\text{Molar mass}}{\text{Empirical formula mass}}$

4. Multiply the subscripts in the empirical formula by the n-factor to get the molecular formula.

Example: Lactic acid (M = 90.08 g/mol) contains 40% C, 6.7% H, and 53.3% O. Find the molecular formula.

Practice Problems

• Empirical formula NPCl2, molar mass 347.64 g/mol. Find the molecular formula.

• Cortisol (M = 362.47 g/mol): 69.6% C, 8.34% H, 22.1% O. Find the molecular formula.

• Compound: 72.2% C, 8.50% H, rest O; 0.250 mol weighs 41.55 g. Find the molecular formula.

Calculating Molar Mass

Molar mass is the mass (in grams) of one mole of a substance. It is calculated by summing the atomic masses of all atoms in the chemical formula.

• SI unit: g/mol

• Also called molecular weight or formula weight.

Steps to Calculate Molar Mass

1. Count the number of each element in the formula (distribute subscripts as needed).

2. Find atomic masses from the Periodic Table.

3. Multiply the number of each atom by its atomic mass.

4. Add the totals to get the molar mass.

Example: Calculate the molar mass of (NH4)2SO4:

$\text{Molar mass} = 2 \times 14.01\ \text{g/mol (N)} + 8 \times 1.008\ \text{g/mol (H)} + 1 \times 32.07\ \text{g/mol (S)} + 4 \times 16.00\ \text{g/mol (O)}$

Practice Problems

• Calculate the molecular weight of C3H5N3O3.

• Find the molar mass of NiCl2·6H2O (nickel(II) chloride hexahydrate).

• Diazepam (Valium): If 0.05570 mol weighs 15.86 g, what is the molar mass?

The Mole Concept

The mole is a counting unit in chemistry, defined as the amount of substance containing as many entities (atoms, molecules, ions, or formula units) as there are atoms in 12.00 g of carbon-12.

• 1 mole = 6.022 x 1023 particles (Avogadro's number).

• Atom: Single element, no charge.

• Ion: Single element with a positive or negative charge.

• Molecule: Two or more atoms bonded together.

• Formula unit: Simplest ratio of ions in an ionic compound.

Converting Between Moles and Particles

• 1 mole = 6.022 x 1023 particles (atoms, molecules, ions, or formula units).

• To convert moles to particles: multiply by Avogadro's number.

• To convert particles to moles: divide by Avogadro's number.

Example: How many moles are in 8.33 x 1037 molecules? $\text{Moles} = \frac{8.33 \times 10^{37}}{6.022 \times 10^{23}}$

Converting Between Mass and Moles

• 1 mole of a substance has a mass equal to its molar mass (in grams).

• To convert grams to moles: divide by molar mass.

• To convert moles to grams: multiply by molar mass.

Example: How many grams of Cl2 are in 2.34 moles? $\text{Mass} = 2.34\ \text{mol} \times 70.90\ \text{g/mol}$

Converting Between Mass and Particles

• Use the mole as a bridge: grams ↔ moles ↔ particles.

Example: How many grams of Cl2 contain 9.25 x 1024 molecules?

Practice Problems

• How many formula units in 73.1 kg NaCl?

• How many oxygen atoms in 783.9 g NiCl2·6H2O?

• How many water molecules in 1.50 x 103 μL of water (density = 1.00 g/mL)?

• How many copper atoms in a 5.160 cm wire (diameter 0.0750 in, density 8.96 g/cm3)?

• How many hydrogen molecules in the sun (density 1.41 g/cm3, volume 1.41 x 1027 m3)?

Mass Percent (Percent Composition)

Mass percent (or weight percent) is the percentage by mass of each element in a compound. It is calculated as:

$\text{Mass percent} = \frac{\text{mass of element in 1 mole of compound}}{\text{mass of 1 mole of compound}} \times 100\%$

• Used to determine the composition of compounds and to calculate empirical formulas.

Example: Calculate the mass percent of carbon in Na2CO3.

Practice Problems

• Find the percent composition of nitrogen and oxygen in NO2.